The new theory and technique of Multi-Addressed Fiber Bragg Structure (MAFBS) usage in Microwave Photonics Sensor Systems (MPSS) is presented. This theory is the logical evolution of the theory of Addressed Fiber Bragg Structure (AFBS) usage as sensors in MPSS. The mathematical model of additive response from a single MAFBS is presented. The MAFBS is a special type of Fiber Bragg Gratings (FBG), the reflection spectrum of which has three (or more) narrow notches. The frequencies of narrow notches are located in the infrared range of electromagnetic spectrum, while differences between them are located in the microwave frequency range. All cross-differences between optical frequencies of single MAFBS are called the address frequencies set. When the additive optical response from a single MAFBS, passed through an optic filter with an oblique amplitude–frequency characteristic, is received on a photodetector, the complex electrical signal, which consists of all cross-frequency beatings of all optical frequencies, which are included in this optical signal, is taken at its output. This complex electrical signal at the photodetector’s output contains enough information to determine the central frequency shift of the MAFBS. The method of address frequencies analysis with the microwave-photonic measuring conversion method, which allows us to define the central frequency shift of a single MAFBS, is discussed in the work.

The design and usage of the addressed combined fiber-optic sensors (ACFOSs) and the multisensory control systems of the greenhouse gas concentration on their basis are investigated herein. The main development trend of the combined fiber-optic sensors (CFOSs), which consists of the fiber Bragg grating (FBG) and the Fabry–Perot resonator (FPR), which are successively formed at the optical fiber end, is highlighted. The use of the addressed fiber Bragg structures (AFBSs) instead of the FBG in the CFOSs not only leads to the significant cheapening of the sensor system due to microwave photonics interrogating methods, but also increasing its metrological characteristics. The structural scheme of the multisensory gas concentration monitoring system is suggested. The suggested scheme allows detecting four types of greenhouse gases (CO₂, NO₂, CH₄ and O_x) depending on the material and thickness of the polymer film, which is the FPR sensitive element. The usage of the Karhunen–Loève transform (KLT), which allows separating each component contribution to the reflected spectrum according to its efficiency, is proposed. In the future, this allows determining the gas concentration at the AFBS address frequencies. The estimations show that the ACFOS design in the multisensory system allows measuring the environment temperature in the range of −60…+300 °C with an accuracy of 0.1–0.01 °C, and the gas concentration in the range of 10…90% with an accuracy of 0.1–0.5%.

Nonlinear spectrum distortions are caused by the peculiarities of the operation of charge-coupled device elements (CCD), in which the signal exposition time (Time of INTegration–TINT) is one of the significant parameters. A change of TINT on a CCD leads to a nonlinear distortion of the resulting spectrum. A nonlinear distortion of the spectrum, in turn, leads to errors in determining the central wavelength of fiber Bragg gratings (FBGs) and spectrally sensitive sensors, which, in general, negatively affects the accuracy of the measuring systems. This paper proposes an algorithm for correcting the nonlinear distortions of the spectrum obtained on a spectrum analyzer using CCD as a receiver. It is shown that preliminary calibration of the optical spectrum analyzer with subsequent mathematical processing of the signal makes it possible to make corrections in the resulting spectrum, thereby leveling the errors caused by measurements at different TINT.

The work is dedicated to a comparative analysis of the following methods for fiber Bragg grating (FBG) spectral response modeling. The Layer Sweep (LS) method, which is similar to the common layer peeling algorithm, is based on the reflectance and transmittance determination for the plane waves propagating through layered structures, which results in the solution of a system of linear equations for the transmittance and reflectance of each layer using the sweep method. Another considered method is based on the determination of transfer matrices (TM) for the FBG as a whole. Firstly, a homogeneous FBG was modeled using both methods, and the resulting reflectance spectra were compared to the one obtained via a specialized commercial software package. Secondly, modeling results of a π-phase-shifted FBG were presented and discussed. For both FBG models, the influence of the partition interval of the LS method on the simulated spectrum was studied. Based on the analysis of the simulation data, additional required modeling conditions for phase-shifted FBGs were established, which enhanced the modeling performance of the LS method.

This paper discusses novel approaches to the numerical integration of the coupled nonlinear Schrödinger equations system for few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes’ interactions. In this case, the coupled nonlinear Schrödinger equation system (CNSES) solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails due to the non-stability of the computing scheme. Owing to this, here we use the combined explicit/implicit finite-difference integration scheme, which is based on the implicit Crank–Nicolson finite-difference scheme. It ensures the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has a higher performance (resolution)—up to three times or more in comparison with the split-step Fourier method—since there is no need to produce direct and inverse Fourier transforms at each integration step. The key advantage of the developed approach is the calculation of any number of modes propagated in the fiber.

This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system, different from the generally accepted approach based on the method of splitting according to physical processes. A combined explicit/implicit finite-difference integration scheme based on the implicit Crank–Nicolson finite-difference scheme is proposed and substantiated. It allows the integration of a nonlinear system of equations with a choice of nonlinear terms from the previous integration step. The main advantages of the proposed method are: its absolute stability through the use of an implicit finite-difference integration scheme and an integrated mechanism for refining the numerical solution at each step; integration with automatic step selection; performance gains (or resolutions) up to three or more orders of magnitude due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step, as is required in the method of splitting according to physical processes. An additional advantage of the proposed method is the ability to calculate the interaction with an arbitrary number of propagation modes in the fiber.